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%I #26 Nov 21 2022 08:42:46
%S 1,2,5,11,27,60,147,344,839,2031,5017,12379,30921,77407,195121,493451,
%T 1253613,3194303,8166757,20933754,53798919,138566312,357647565,
%U 924834079,2395702801,6215748612,16150985071,42024182520,109485000777,285578913962,745728542725
%N -a(n) is inverse EULER transform of -A000041(n).
%H Alois P. Heinz, <a href="/A095975/b095975.txt">Table of n, a(n) for n = 1..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Moebius transform of A055890(n).
%F a(n) ~ d^n / n, d = 2.69832910647421123126399866618837... (see A246828). - _Vaclav Kotesovec_, Aug 25 2014
%p with(numtheory): b:= proc(n) option remember; `if`(n=0,1, add(add(d, d=divisors(j)) *b(n-j), j=1..n)/n) end: c:= proc(n) option remember; local j; add(c(j) *b(n-j), j=1..n-1)-n*b(n) end: a:= -proc(n) option remember; local d; `if`(n=0,1, add(mobius(n/d)*c(d), d=divisors(n))/n) end: seq(a(n), n=1..40); # _Alois P. Heinz_, Sep 09 2008
%p # The function EulerInvTransform is defined in A358451.
%p a := -EulerInvTransform(n -> -combinat:-numbpart(n)):
%p seq(a(n), n = 1..31); # _Peter Luschny_, Nov 21 2022
%t b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d, {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; c[n_] := c[n] = Sum[c[j]*b[n-j], {j, 1, n-1}] - n*b[n]; a[n_] := -If[n == 0, 1, Sum[MoebiusMu[n/d]*c[d], {d, Divisors[n]}]/n]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Feb 24 2015, after _Alois P. Heinz_ *)
%Y Cf. A055887, A246828.
%K easy,nonn
%O 1,2
%A _Vladeta Jovovic_, Jul 20 2004
%E More terms from _Alois P. Heinz_, Sep 09 2008
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